An Estimate of the Influence of Breaking Waves on the Dynamics of the Upper Ocean

  • Norden E. Huang


The influence of breaking waves on the dynamics of the upper ocean is estimated using the concept of an energy balance between the wind and waves. The rate of energy release from wave breaking is calculated by the statistical model proposed by Longuet-Higgins (1969). It is found that the result of this calculation depends only on one parameter, the significant slope, defined and used by Huang and Long (1980). Treating the energy released from the breaking waves as the sole source of turbulent energy, various models are constructed to simulate a wide variety of dynamical phenomena in the upper ocean layer. The quantities calculated from these models include surface drift, whitecapping percentage, and mixing efficiency. This treatment using breaking waves as the sole turbulent energy source is only a first-order approximation to reality but the technique does result in the first quantitative estimates of the effect of breaking waves on upper ocean layer dynamics. One of the advantages of using the present approach is that the inputs to the models are all obtainable from remote sensors. Possible future extensions and improvements to the models are also discussed. It is believed that the models presented here offer a new look for the study of the dynamics of the upper ocean. Additional studies and the attention of future investigators are required to bring this technique to full fruition.


Mixed Layer Wind Stress Dissipation Rate Wave Field Wave Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Benilov, A. Y. (1973): Generation of ocean turbulence by surface waves. Izv. Atmos. Ocean Phys. 9, 293–303.Google Scholar
  2. Bye, J. A. T. (1967): The wave-drift current. J. Mar. Res. 25, 95–102.Google Scholar
  3. Cokelet, E. D. (1977a): Breaking waves. Nature 267, 769–774.CrossRefGoogle Scholar
  4. Cokelet, E. D. (1977b): Steep gravity waves in water of arbitrary uniform depth. Philos. Trans. R. Soc. London Ser. A 286, 183–230.MathSciNetMATHCrossRefGoogle Scholar
  5. Davis, R. E., R. deSzoeke, and P. Nüler (1981): Variability in the upper ocean during MILE. Part II. Modeling the mixed layer response. Deep-Sea Res. 28, 1453–1475.CrossRefGoogle Scholar
  6. Denman, K. L. (1973): A time-dependent model of the upper ocean. J. Phys. Oceanogr. 3, 173–184.CrossRefGoogle Scholar
  7. deSzoeke, R., and P. B. Rhines (1976): Asymptotic regimes in mixed-layer deepening. J. Mar. Res. 34, 111–116.Google Scholar
  8. Dillon, T. M., and D. R. Caldwell (1978): Catastrophic events in a surface mixed layer. Nature 276, 601–602.CrossRefGoogle Scholar
  9. Ekman, V. W. (1905): On the influence of the earth’s rotation on ocean-current. Ark. Math. Astron. Ocean. Phys. 2, (11).Google Scholar
  10. Fenton, J. D. (1972): A ninth-order solution for the solitary wave. J. Fluid Mech. 53, 257–271.MATHCrossRefGoogle Scholar
  11. Fenton, J. D. (1979): A higher-order cnoidal wave theory. J. Fluid Mech. 94, 129–161.MathSciNetMATHCrossRefGoogle Scholar
  12. Garnich, N. G., and S. A. Kitaigorodskii (1977): On the rate of deepening of the oceanic mixed layer. Izv. Atmos. Ocean Phys. 13, 888–893.Google Scholar
  13. Garwood, R. W., Jr. (1979): Air-Sea interaction and dynamics of the surface mixed layer. Rev. Geophys. Space Phys. 17, 1507–1524.CrossRefGoogle Scholar
  14. Grant, H. L., A. Moilhet, and W. M. Vogel (1968): Some observations on the occurrence of turbulence in and above the thermocline. J. Fluid Mech. 34, 443–448.CrossRefGoogle Scholar
  15. Hasselmann, K., D. B. Ross, P. Müller, and W. Sell (1976): A parametric wave prediction model. J. Phys. Oceanogr. 6, 200–228.CrossRefGoogle Scholar
  16. Holland, W. R. (1977): The role of the upper ocean as a boundary layer in models of the oceanic general circulation. Modelling and Prediction of the Upper Layer of the Ocean (E. B. Kraus, ed.), Pergamon Press, Elmsford, New York, 7–30.Google Scholar
  17. Huang, N. E. (1979): On surface drift current in the ocean. J. Fluid Mech. 91, 191–208.MATHCrossRefGoogle Scholar
  18. Huang, N. E., and S. R. Long (1980): An experimental study of the surface elevation probability distribution and statistics of wind generated waves. J. Fluid Mech. 101, 179–200.CrossRefGoogle Scholar
  19. Huang, N. E., S. R. Long, C. C. Tung, T. Yuen, and L. F. Bliven (1981a): A unified two-parameter wave spectral model for a general sea state. J. Fluid Mech. 112, 203–224.MATHCrossRefGoogle Scholar
  20. Huang, N. E., S. R. Long, and L. F. Bliven (1981b): On the importance of the significant slope in empirical wind wave studies. J. Oceanogr. 11, 569–573.CrossRefGoogle Scholar
  21. Kato, H., and O. Philhps (1969): On the penetration of a turbulent layer into stratified fluid. J. Fluid Mech. 37, 634–655.CrossRefGoogle Scholar
  22. Kenyon, K. E. (1970): Stokes transport. J. Geophys. Res. 75, 1133–1135.CrossRefGoogle Scholar
  23. Kitaigorodskii, S. A. (1973): The Physics of Air-Sea Interaction, Isr. Progr. Sci. Transl., Jerusalem.Google Scholar
  24. Kitaigorodskii, S. A. (1979): Review of the theories of wind-mixed layer deepening. Marine Forecasting (J. C. J. Nihoul, ed.), Elsevier, Amsterdam, 1–33.Google Scholar
  25. Kitaigorodskii, S. A., and Y. Z. Miropolskii (1968): Turbulent-energy dissipation in the ocean surface layer. Izv. Atmos. Ocean Phys. 4, 647–659.Google Scholar
  26. Kraus, E. B., and J. S. Turner (1967): A one-dimensional model of the seasonal thermocline. IL The general theory and its consequences. Tellus 19, 98–106.CrossRefGoogle Scholar
  27. Longuet-Higgins, M. S. (1962): The statistical geometry of random surface. Hydrodynamics Stability: Proc. 13th Symp. Appl. Math. 105–144.Google Scholar
  28. Longuet-Higgins, M. S. (1969): On wave breaking and the equilibrium spectrum of wind-generated waves. Proc. R. Soc. London Ser. A 310, 151–159.CrossRefGoogle Scholar
  29. Longuet-Higgins, M. S., and E. D. Cokelet (1976): The deformation of steep surface waves. L A numerical method of computation. Proc. R. Soc. London Ser. A 350, 1–26.MathSciNetMATHCrossRefGoogle Scholar
  30. Longuet-Higgins, M. S., and E. D. Cokelet (1978): The deformation of steep surface waves. XL Growth of normal-mode instabilities. Proc. R. Soc. London Ser. A 364, 1–28.MathSciNetMATHCrossRefGoogle Scholar
  31. Longuet-Higgins, M. S., and M. J. H. Fox (1977): Theory of the almost-highest waves: The inner solution. J. Fluid Mech. 80, 721–742.MathSciNetMATHCrossRefGoogle Scholar
  32. Miropolskii, Y. Z. (1970): Nonstationary model of the wind-convection mixing layer in the ocean. Izv. Atmos. Ocean Phys. 6, 1284–1294.Google Scholar
  33. Mitsuyasu, H., and T. Honda (1975): The high frequency spectrum of wind-generated waves. Rep. Res. Inst. Appl. Mech. Krushu Univ. 22, 327–355.Google Scholar
  34. Monahan, E. C. (1971): Oceanic whitecaps. J. Phys. Oceanogr. 1, 139–144.CrossRefGoogle Scholar
  35. Monahan, E. C., and L O. Muircheartaigh (1980): Optimal power-law description of oceanic whitecap coverage dependence on wind speed. J. Phys. Oceanogr. 10, 2094–2099.CrossRefGoogle Scholar
  36. Monin, A. S. (1977): On the generation of oceanic turbulence. Izv. Atmos. Ocean Phys. 13, 798–803.Google Scholar
  37. Müller, P. (1976): Parameterization of one-dimensional wind wave spectra and their dependence on the state of development. Hamburger Geophysikalische Einzelschriften Heft 31, Wittenbom Sohne, Hamburg.Google Scholar
  38. Navrotskii, V. V. (1967): Waves and turbulence in the ocean surface layer. Oceanology 6, 755–766.Google Scholar
  39. Nüler, P. P. (1977): One-dimensional models of the seasonal thermocline. The Sea, Vol. 6 (E. D. Goldberg, L N. McCave, J. J. O’Brien, and J. H. Steele, eds. X Wiley-Interscience, New York.Google Scholar
  40. Nüler, P. P., and E. B. Kraus (1977): One-dimensional models of the upper ocean. Modelling and Prediction of the Upper Layers of the Ocean (E. B. Kraus, ed.), Pergamon Press, Elmsford, New York, 143–172.Google Scholar
  41. Phillips, O. M. (1961): A note on the turbulence generated by gravity waves, J. Geophys. Res. 66, 2889–2893.MathSciNetCrossRefGoogle Scholar
  42. Phillips, O. M. (1977): The Dynamics of the Upper Ocean, 2nd ed., Cambridge University Press, London.MATHGoogle Scholar
  43. Phillips, O. M., and M. L. Banner (1974): Wave breaking in the presence of wind drift and swell. J. Fluid Mech. 66, 625–640.MATHCrossRefGoogle Scholar
  44. Pollard, R. T., and R. C. Millard, Jr. (1970): Comparison between observed and simulated wind-generated inertial oscillations. Deep-Sea Res. 17, 813–821.Google Scholar
  45. Pollard, R. T., P. B. Rhines, and R. O. R. Y. Thompson (1973): The deepening of the wind-mixed layer. Geophys. Fluid Dyn. 4, 381–404.Google Scholar
  46. Richman, J., and C. Garrett (1977): The transfer of energy and momentum by the wind to the surface mixed layer. J. Phys. Oceanogr. 7, 876–881.CrossRefGoogle Scholar
  47. Ross, D. B., and V. Cardone (1974): Observations of oceanic whitecaps and their relation to remote measurements of surface wind speed. J. Geophys. Res. 79, 444–452.CrossRefGoogle Scholar
  48. Schwartz, L. W. (1974): Computer extension and analytic continuation of Stokes’ expansion for gravity waves. J. Fluid Mech. 62, 553–578.MATHCrossRefGoogle Scholar
  49. Shonting, D. H. (1965): A prehminary investigation of momentum flux in ocean waves. Pure Appl. Geophys. 57, 149–152.CrossRefGoogle Scholar
  50. Steele, J. (1977): Ecological modeling of the upper layers. Modelling and Prediction of the U pper Layers of the Ocean (E. B. Kraus, ed.), Pergamon Press, Elmsford, N.Y., 243–250.Google Scholar
  51. Stoker, J. J. (1957): Water Waves, Wiley-Interscience, New York.MATHGoogle Scholar
  52. Stokes, G. G. (1847): On the theory of oscillatory waves. Trans. Cambridge Philos. Soc. 8, 441–455.Google Scholar
  53. Stokes, G. G. (1880): Considerations relative to the greatest height of oscillatory waves which can be propagated without change of form. Math and Physics Papers 1, 225–228, Cambridge University Press, London.Google Scholar
  54. Thompson, R. O. R. Y. (1982): A potential-flow model of turbulence caused by breaking surface waves. J. Geophys. Res. 87, 1935–1938.CrossRefGoogle Scholar
  55. Thorpe, S. A., and P. N. Humpries (1979): Bubbles and breaking waves. Nature 283, 463–465.CrossRefGoogle Scholar
  56. Thorpe, S. A., and A. R. Stubbs (1979): Bubbles in a freshwater lake. Nature 279, 403–405.CrossRefGoogle Scholar
  57. Turner, J. S. (1969): A note on wind mixing at the seasonal thermocline. Deep-Sea Res. 16 (Suppl.), 287–300.Google Scholar
  58. Walsh, E. J. (1979): Extraction of ocean wave height and dominant wavelength from GEOS-3 altimeter data. J. Geophys. Res. 84, 4003–4010.CrossRefGoogle Scholar
  59. Wu, J. (1973): Wind-induced turbulent entrainment across a stable density interface. J. Fluid Mech. 61, 275–287CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Norden E. Huang
    • 1
  1. 1.NASA Goddard Space Flight CenterGreenbeltUSA

Personalised recommendations